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/* multiroots/dnewton.c
*
* Copyright (C) 1996, 1997, 1998, 1999, 2000 Brian Gough
*
* This program is free software; you can redistribute it and/or modify
* it under the terms of the GNU General Public License as published by
* the Free Software Foundation; either version 2 of the License, or (at
* your option) any later version.
*
* This program is distributed in the hope that it will be useful, but
* WITHOUT ANY WARRANTY; without even the implied warranty of
* MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the GNU
* General Public License for more details.
*
* You should have received a copy of the GNU General Public License
* along with this program; if not, write to the Free Software
* Foundation, Inc., 51 Franklin Street, Fifth Floor, Boston, MA 02110-1301, USA.
*/
#include <config.h>
#include <stddef.h>
#include <stdlib.h>
#include <stdio.h>
#include <math.h>
#include <float.h>
#include <gsl/gsl_math.h>
#include <gsl/gsl_errno.h>
#include <gsl/gsl_multiroots.h>
#include <gsl/gsl_linalg.h>
/* Newton method using a finite difference approximation to the jacobian.
The derivatives are estimated using a step size of
h_i = sqrt(DBL_EPSILON) * x_i
*/
typedef struct
{
gsl_matrix * J;
gsl_matrix * lu;
gsl_permutation * permutation;
}
dnewton_state_t;
static int dnewton_alloc (void * vstate, size_t n);
static int dnewton_set (void * vstate, gsl_multiroot_function * function, gsl_vector * x, gsl_vector * f, gsl_vector * dx);
static int dnewton_iterate (void * vstate, gsl_multiroot_function * function, gsl_vector * x, gsl_vector * f, gsl_vector * dx);
static void dnewton_free (void * vstate);
static int
dnewton_alloc (void * vstate, size_t n)
{
dnewton_state_t * state = (dnewton_state_t *) vstate;
gsl_permutation * p;
gsl_matrix * m, * J;
m = gsl_matrix_calloc (n,n);
if (m == 0)
{
GSL_ERROR ("failed to allocate space for lu", GSL_ENOMEM);
}
state->lu = m ;
p = gsl_permutation_calloc (n);
if (p == 0)
{
gsl_matrix_free(m);
GSL_ERROR ("failed to allocate space for permutation", GSL_ENOMEM);
}
state->permutation = p ;
J = gsl_matrix_calloc (n,n);
if (J == 0)
{
gsl_permutation_free(p);
gsl_matrix_free(m);
GSL_ERROR ("failed to allocate space for d", GSL_ENOMEM);
}
state->J = J;
return GSL_SUCCESS;
}
static int
dnewton_set (void * vstate, gsl_multiroot_function * function, gsl_vector * x, gsl_vector * f, gsl_vector * dx)
{
dnewton_state_t * state = (dnewton_state_t *) vstate;
size_t i, n = function->n ;
int status;
status = GSL_MULTIROOT_FN_EVAL (function, x, f);
if (status)
return status;
status = gsl_multiroot_fdjacobian (function, x, f, GSL_SQRT_DBL_EPSILON,
state->J);
if (status)
return status;
for (i = 0; i < n; i++)
{
gsl_vector_set (dx, i, 0.0);
}
return GSL_SUCCESS;
}
static int
dnewton_iterate (void * vstate, gsl_multiroot_function * function, gsl_vector * x, gsl_vector * f, gsl_vector * dx)
{
dnewton_state_t * state = (dnewton_state_t *) vstate;
int signum ;
size_t i;
size_t n = function->n ;
gsl_matrix_memcpy (state->lu, state->J);
{
int status = gsl_linalg_LU_decomp (state->lu, state->permutation, &signum);
if (status)
return status;
}
{
int status = gsl_linalg_LU_solve (state->lu, state->permutation, f, dx);
if (status)
return status;
}
for (i = 0; i < n; i++)
{
double e = gsl_vector_get (dx, i);
double y = gsl_vector_get (x, i);
gsl_vector_set (dx, i, -e);
gsl_vector_set (x, i, y - e);
}
{
int status = GSL_MULTIROOT_FN_EVAL (function, x, f);
if (status != GSL_SUCCESS)
{
return GSL_EBADFUNC;
}
}
gsl_multiroot_fdjacobian (function, x, f, GSL_SQRT_DBL_EPSILON, state->J);
return GSL_SUCCESS;
}
static void
dnewton_free (void * vstate)
{
dnewton_state_t * state = (dnewton_state_t *) vstate;
gsl_matrix_free(state->J);
gsl_matrix_free(state->lu);
gsl_permutation_free(state->permutation);
}
static const gsl_multiroot_fsolver_type dnewton_type =
{"dnewton", /* name */
sizeof (dnewton_state_t),
&dnewton_alloc,
&dnewton_set,
&dnewton_iterate,
&dnewton_free};
const gsl_multiroot_fsolver_type * gsl_multiroot_fsolver_dnewton = &dnewton_type;
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